§
    JŠtjX  ã                   ó®  — d dl Z d dlZddlmZmZmZmZmZ ej	        Z
i fd„Z G d„ de¦  «        Z ed¦  «        Z ed¦  «        Z ed	¦  «        Z ed
¦  «        Z ed¦  «        Z ed¦  «        Z ed¦  «        Z ed¦  «        Z ed¦  «        Z ed¦  «        Z ed¦  «        Z	 d dlZej                             e¦  «         dS # e$ r Y dS w xY w)é    Né   )Ú	int_typesÚmpf_hashÚbitcountÚfrom_man_expÚHASH_MODULUSc                 óæ   — | |f}||v r||         S | |}}|r	|||z  }}|°	|dk    r
| |z  } ||z  }t          t          ¦  «        }| |f|_        |dk    rt          |d         ¦  «        dk     r|||<   |S )Nr   é   r   éd   )ÚnewÚmpqÚ_mpq_Úabs)ÚpÚqÚ_cacheÚkeyÚxÚyÚvs          úM/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/mpmath/rational.pyÚcreate_reducedr      s¢   € Ø
ˆQˆ$€CØ
ˆf€}€}Ø�cŒ{ÐØˆa€q€AØ
ð Ø�!�a‘%ˆ1ˆð ð àˆA‚v€vØ	ˆa‰ˆØ	ˆa‰ˆÝ�C‰Œ€AØ�ˆd€A„GàˆA‚v€v•#�c˜!”f‘+”+ Ò#Ð#Øˆˆs‰Ø€Hó    c                   ó°   — e Zd ZdZdgZdd„Zd„ Zd„ Zd„ Zd„ Z	e	Z
d	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ ZeZd„ Zd„ Zd„ ZeZd„ Zd„ Zd„ ZdS )r   zH
    Exact rational type, currently only intended for internal use.
    r   r   c                 óŽ   — t          |¦  «        t          u r|\  }}nt          |d¦  «        r
|j        \  }}t	          ||¦  «        S )Nr   )ÚtypeÚtupleÚhasattrr   r   )Úclsr   r   s      r   Ú__new__zmpq.__new__   sK   € Ý�‰7Œ7•eÐÐØ‰DˆAˆqˆqÝ�Q˜Ñ Ô ð 	Ø”7‰DˆAˆqÝ˜a Ñ#Ô#Ð#r   c                 ó   — d| j         z  S )Nz
mpq(%s,%s)©r   ©Úss    r   Ú__repr__zmpq.__repr__&   s   € Ø˜aœgÑ%Ð%r   c                 ó   — d| j         z  S )Nz(%s/%s)r"   r#   s    r   Ú__str__zmpq.__str__)   s   € Ø˜1œ7Ñ"Ð"r   c                 ó    — | j         \  }}||z  S ©Nr"   )r$   ÚaÚbs      r   Ú__int__zmpq.__int__,   s   € ØŒw‰ˆˆ1Ø�A‰vˆr   c                 ó6   — t          | j        d         ¦  «        S ©Nr   )Úboolr   r#   s    r   Ú__nonzero__zmpq.__nonzero__0   s   € Ý�A”G˜A”JÑÔÐr   c           	      óª  — | j         \  }}t          j        dk    r_t          |t          dz
  t          ¦  «        }|st          j        j        }nt          |¦  «        |z  t          z  }|dk     r| }|dk    rd}|S |dk    rt          |¦  «        S ||dz
  z  s-t          t          |dt          |¦  «        z
  ¦  «        ¦  «        S t          ||f¦  «        S )N©é   é   r4   r   éÿÿÿÿéþÿÿÿr   )r   ÚsysÚversion_infoÚpowr   Ú	hash_infoÚinfr   Úhashr   r   r   )r$   r*   r+   ÚinverseÚhs        r   Ú__hash__zmpq.__hash__5   sÑ   € ØŒw‰ˆˆ1ÝÔ˜vÒ%Ð%Ý˜!�\¨!™^­\Ñ:Ô:ˆGØð 6Ý”MÔ%��å˜‘V”V˜gÑ%­Ñ5�Ø�1Šuˆu˜1˜"�aØ�BŠwˆw˜B˜ØˆHà�AŠvˆvÝ˜A‘w”w�à˜˜1™‘Ið @Ý¥¨Q°µ(¸1±+´+±Ñ >Ô >Ñ?Ô?Ð?Ý˜˜1˜‘;”;Ðr   c                 ó¢   — t          |¦  «        }|t          u r| j        |j        k    S |t          v r| j        \  }}|dk    rdS ||k    S t          S )Nr   F©r   r   r   r   ÚNotImplemented©r$   ÚtÚttyper*   r+   s        r   Ú__eq__z
mpq.__eq__H   sX   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7˜aœgÒ%Ð%Ø•IÐÐØ”7‰DˆAˆqØ�AŠvˆvØ�uØ˜’6ˆMÝÐr   c                 ó¢   — t          |¦  «        }|t          u r| j        |j        k    S |t          v r| j        \  }}|dk    rdS ||k    S t          S )Nr   TrA   rC   s        r   Ú__ne__z
mpq.__ne__S   sX   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7˜aœgÒ%Ð%Ø•IÐÐØ”7‰DˆAˆqØ�AŠvˆvØ�tØ˜’6ˆMÝÐr   c                 óÐ   — t          |¦  «        }|t          v r| j        \  }} ||||z  ¦  «        S |t          u r&| j        \  }}|j        \  }} |||z  ||z  ¦  «        S t          S r)   )r   r   r   r   ÚNotImplementedError)r$   rD   ÚoprE   r*   r+   ÚcÚds           r   Ú_cmpzmpq._cmp^   st   € Ý�Q‘”ˆØ•IÐÐØ”7‰DˆAˆqØ�2�a˜˜1™‘:”:ÐØ•Cˆ<ˆ<Ø”7‰DˆAˆqØ”7‰DˆAˆqØ�2�a˜‘c˜1˜Q™3‘<”<ÐÝ"Ð"r   c                 óB   — |                       |t          j        ¦  «        S r)   )rN   ÚoperatorÚlt©r$   rD   s     r   Ú__lt__z
mpq.__lt__i   ó   € ˜QŸVšV A¥x¤{Ñ3Ô3Ð3r   c                 óB   — |                       |t          j        ¦  «        S r)   )rN   rP   ÚlerR   s     r   Ú__le__z
mpq.__le__j   rT   r   c                 óB   — |                       |t          j        ¦  «        S r)   )rN   rP   ÚgtrR   s     r   Ú__gt__z
mpq.__gt__k   rT   r   c                 óB   — |                       |t          j        ¦  «        S r)   )rN   rP   ÚgerR   s     r   Ú__ge__z
mpq.__ge__l   rT   r   c                 óf   — | j         \  }}|dk    r| S t          t          ¦  «        }| |f|_         |S r.   ©r   r   r   ©r$   r*   r+   r   s       r   Ú__abs__zmpq.__abs__n   s8   € ØŒw‰ˆˆ1Ø�Š6ˆ6ØˆHÝ•‰HŒHˆØ�"�a�%ˆŒØˆr   c                 óV   — | j         \  }}t          t          ¦  «        }| |f|_         |S r)   r_   r`   s       r   Ú__neg__zmpq.__neg__v   s*   € ØŒw‰ˆˆ1Ý•‰HŒHˆØ�"�a�%ˆŒØˆr   c                 ó   — | S r)   © r#   s    r   Ú__pos__zmpq.__pos__|   s   € Øˆr   c                 ó  — t          |¦  «        }|t          u r0| j        \  }}|j        \  }}t          ||z  ||z  z   ||z  ¦  «        S |t          v r/| j        \  }}t          t          ¦  «        }|||z  z   |f|_        |S t          S r)   ©r   r   r   r   r   r   rB   ©r$   rD   rE   r*   r+   rL   rM   r   s           r   Ú__add__zmpq.__add__   ó‹   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7‰DˆAˆqØ”7‰DˆAˆqÝ! ! A¡# a¨¡c¡'¨1¨Q©3Ñ/Ô/Ð/Ø•IÐÐØ”7‰DˆAˆqÝ•C‘”ˆAØ˜˜!™‘e˜Q�hˆAŒGØˆHÝÐr   c                 ó  — t          |¦  «        }|t          u r0| j        \  }}|j        \  }}t          ||z  ||z  z
  ||z  ¦  «        S |t          v r/| j        \  }}t          t          ¦  «        }|||z  z
  |f|_        |S t          S r)   rh   ri   s           r   Ú__sub__zmpq.__sub__Ž   rk   r   c                 ó  — t          |¦  «        }|t          u r0| j        \  }}|j        \  }}t          ||z  ||z  z
  ||z  ¦  «        S |t          v r/| j        \  }}t          t          ¦  «        }||z  |z
  |f|_        |S t          S r)   rh   ri   s           r   Ú__rsub__zmpq.__rsub__›   s‹   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7‰DˆAˆqØ”7‰DˆAˆqÝ! ! A¡# a¨¡c¡'¨1¨Q©3Ñ/Ô/Ð/Ø•IÐÐØ”7‰DˆAˆqÝ•C‘”ˆAØ˜‘c˜!‘e˜Q�hˆAŒGØˆHÝÐr   c                 óà   — t          |¦  «        }|t          u r*| j        \  }}|j        \  }}t          ||z  ||z  ¦  «        S |t          v r| j        \  }}t          ||z  |¦  «        S t
          S r)   ©r   r   r   r   r   rB   ©r$   rD   rE   r*   r+   rL   rM   s          r   Ú__mul__zmpq.__mul__¨   ót   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7‰DˆAˆqØ”7‰DˆAˆqÝ! ! A¡# q¨¡sÑ+Ô+Ð+Ø•IÐÐØ”7‰DˆAˆqÝ! ! A¡# qÑ)Ô)Ð)ÝÐr   c                 óà   — t          |¦  «        }|t          u r*| j        \  }}|j        \  }}t          ||z  ||z  ¦  «        S |t          v r| j        \  }}t          |||z  ¦  «        S t
          S r)   rq   rr   s          r   Ú__div__zmpq.__div__µ   st   € Ý�Q‘”ˆØ•Cˆ<ˆ<Ø”7‰DˆAˆqØ”7‰DˆAˆqÝ! ! A¡# q¨¡sÑ+Ô+Ð+Ø•IÐÐØ”7‰DˆAˆqÝ! ! Q q¡SÑ)Ô)Ð)ÝÐr   c                 óà   — t          |¦  «        }|t          u r*| j        \  }}|j        \  }}t          ||z  ||z  ¦  «        S |t          v r| j        \  }}t          ||z  |¦  «        S t
          S r)   rq   rr   s          r   Ú__rdiv__zmpq.__rdiv__À   rt   r   c                 óÊ   — t          |¦  «        }|t          v rE| j        \  }}|r2|dk     r||| }}}t          t          ¦  «        }||z  ||z  f|_        |S t
          ‚t          S r.   )r   r   r   r   r   ÚZeroDivisionErrorrB   )r$   rD   rE   r*   r+   r   s         r   Ú__pow__zmpq.__pow__Ë   sr   € Ý�Q‘”ˆØ•IÐÐØ”7‰DˆAˆqØð Ø�q’5�5Ø  Q B˜!�q�AÝ�‘H”H�Ø˜Q™$  1¡˜*�”Ø�Ý#Ð#ÝÐr   N)r   )Ú__name__Ú
__module__Ú__qualname__Ú__doc__Ú	__slots__r    r%   r'   r,   r0   Ú__bool__r?   rF   rH   rN   rS   rW   rZ   r]   ra   rc   rf   rj   Ú__radd__rm   ro   rs   Ú__rmul__rv   rx   r{   re   r   r   r   r      s„  € € € € € ðð ð �	€Ið$ð $ð $ð $ð&ð &ð &ð#ð #ð #ðð ð ð ð  ð  ð €Hðð ð ð&	ð 	ð 	ð	ð 	ð 	ð	#ð 	#ð 	#ð 4Ð3Ð3Ø3Ð3Ð3Ø3Ð3Ð3Ø3Ð3Ð3ðð ð ðð ð ðð ð ðð ð ð €Hðð ð ðð ð ð	ð 	ð 	ð €Hð	ð 	ð 	ð	ð 	ð 	ðð ð ð ð r   r   )r   r   )r   r   )r   r4   r2   )r   r
   )r   é   )r3   r„   )é   r4   )r3   r
   )é   r
   )r…   r
   )rP   r7   Úlibmpr   r   r   r   r   Úobjectr    r   r   r   Úmpq_1Úmpq_0Úmpq_1_2Úmpq_3_2Úmpq_1_4Úmpq_1_16Úmpq_3_16Úmpq_5_2Úmpq_3_4Úmpq_7_4Úmpq_5_4ÚnumbersÚRationalÚregisterÚImportErrorre   r   r   ú<module>r˜      sp  ðØ €€€Ø 
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Ø LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ LÐ Là„n€à "ð ð ð ð ð"~ð ~ð ~ð ~ð ~ˆ&ñ ~ô ~ð ~ðB 	ˆˆE‰
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ˆ#ˆe‰*Œ*€ð	Ø€N€N€NØÔ×Ò˜cÑ"Ô"Ð"Ð"Ð"øØð 	ð 	ð 	Ø€D€Dð	øøøs   Â+C ÃCÃC